Question

Ashley participated in a triathlon: she swam for 10 minutes at the rate of 40 meters/minute. Then she biked for 40 minutes at the rate of 400 meters/minute. Finally she ran for 25 minutes at the rate of 200 meters/minute. Write a piecewise function expressing the distance d(t) traveled as function of time t

Answer 1

A piecewise function is a function that is applied depending on the

particular interval of the domain.

A piecewise function for the journey can be presented as follows;

• $& d(t) = 40\cdot t \text{ if } t\leq 10 \\ \\ &d(t) =400 + 400 \cdot t \text{ if } 10 <t\leq 50 \\ \\ & d(t) = 16,400 + 200 \cdot t \text{ if } 60 <t\leq 85 \end{cases}$

Reasons:

The duration of swimming = 10 minutes

The speed with which she swam = 40 meters /minute

The duration of biking = 40 minutes

The rate at which she biked = 400 meters/minute

The distance in which she ran = 25 minutes

The rate at which she ran = 200 meters/minute

Therefore;

Distance in which Ashley swam, $D_{swim}$ = 10 minutes × 40 m/min = 400 m

Distance of biking, $D_{bike}$ = 40 minutes × 400 m/min = 16,000 m

The distance she ran, $D_{run}$ = 25 minutes × 200 m/minute = 5,000 meters

The time during which she swam = The first 10 minutes = t ≤ 10

The time in which she biked =40 minutes = From 10 minutes to 50 minutes = 10 < t ≤ 50

The time in which she ran after start is 50 < t ≤ 85

Therefore the piecewise function of the above information can be presented as follows;

$& d(t) = 40 \times t \text{ if } t\leq 10 \\ \\ &d(t) =400 + 400 \times t \text{ if } 10 <t\leq 50 \\ \\ & d(t) = 16,400 + 200 \times t \text{ if } 60 <t\leq 85 \end{cases}$

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